Geometry Olympiad: geometry challenge problems #geometry #shorts

[cmarrigoni]

The main triangle is a 3-4-5 triangle, and due to the nature of the square in relation to the large triangle, all of the small triangles are also 3-4-5 triangles. If we denote the length of the side of the square as X, we can break down the length of the 4 units side of the large triangle to 4/5x + 4/3x = 4 solving for x, we find that x = 15/8 units. Therefore the area of the square is x^2 = (15/8)^2 = 3.515625 units

[sasikumark]

Area of the triangle = 1÷2 ×base×height

By Pythagoras theorem, height = 3
Area of the triangle = 1÷2×4×3 = 6 sq. units